Q. 96 - Precalculus Enhanced with Graphing Utilities

Question

The area under the curve $y=\sqrt{x}$ bounded below by the $x$-axis and on the right by $x=4$ is $\frac{16}{3}$ square units. Using the ideas presented in this section, what do you think is the area under the curve of $y=\sqrt{-x}$ bounded below by the $x$-axis and on the left by $x=-4$ ? Justify your answer.

Step-by-Step Solution

Answer

The area is same for both the functions

Step 1: Given information

Given the equation $$\begin{gathered} y=\sqrt{x}, \\ y=\sqrt{-x} \end{gathered}$$

Step 2: Checking the areas

The graph is 

Step 3: Checking the area

The graph of $y=\sqrt{-x}$ is 

The graphs are reflection of each other so the area is same for both the functions